Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 12}{x - 10} = \dfrac{8x + 32}{x - 10}$
Explanation: Multiply both sides by $x - 10$ $ \dfrac{x^2 + 12}{x - 10} (x - 10) = \dfrac{8x + 32}{x - 10} (x - 10)$ $ x^2 + 12 = 8x + 32$ Subtract $8x + 32$ from both sides: $ x^2 + 12 - (8x + 32) = 8x + 32 - (8x + 32)$ $ x^2 + 12 - 8x - 32 = 0$ $ x^2 - 20 - 8x = 0$ Factor the expression: $ (x - 10)(x + 2) = 0$ Therefore $x = 10$ or $x = -2$ However, the original expression is undefined when $x = 10$. Therefore, the only solution is $x = -2$.